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A127448 Triangle T(n,k) read by rows: matrix product A054525 * A127648.

%I A127448 #10 Jan 07 2015 10:03:08
%S A127448 1,-1,2,-1,0,3,0,-2,0,4,-1,0,0,0,5,1,-2,-3,0,0,6,-1,0,0,0,0,0,7,0,0,0,
%T A127448 -4,0,0,0,8,0,0,-3,0,0,0,0,0,9,1,-2,0,0,-5,0,0,0,0,10,-1,0,0,0,0,0,0,
%U A127448 0,0,0,11,0,2,0,-4,0,-6,0,0,0,0,0,12,-1,0,0,0,0,0,0,0,0,0,0,0,13,1,-2,0,0,0,0,-7,0,0,0,0,0,0
%N A127448 Triangle T(n,k) read by rows: matrix product A054525 * A127648.
%F A127448 T(n,k) = sum _{j=k..n} A054525(n,j)*A127648(j,k) = k*A054525(n,k).
%F A127448 sum_{k=1..n} T(n,k) = A000010(n) (row sums).
%F A127448 T(n,1) = A008683(n).
%e A127448 First few rows of the triangle are;
%e A127448 1;
%e A127448 -1, 2;
%e A127448 -1, 0, 3;
%e A127448 0, -2, 0, 4;
%e A127448 -1, 0, 0, 0, 5;
%e A127448 1, -2, -3, 0, 0, 6;
%e A127448 -1, 0, 0, 0, 0, 0, 7;
%e A127448 0, 0, 0, -4, 0, 0, 0, 8;
%e A127448 0, 0, -3, 0, 0, 0, 0, 0, 9;
%e A127448 1, -2, 0, 0,-5, 0, 0, 0, 0, 10;
%e A127448 ...
%p A127448 A127648 := proc(n,k) if n = k then n; else 0 ; fi; end:
%p A127448 A054525 := proc(n,k) if k = n then 1; elif n mod k = 0 then numtheory[mobius](n/k) ; else 0 ; fi; end:
%p A127448 A127448 := proc(n,k) add( A054525(n,j)*A127648(j,k), j=k..n) ; end: seq(seq( A127448(n,k),k=1..n),n=1..15) ;
%Y A127448 Cf. A000010, A008683, A051731.
%K A127448 tabl,sign,easy
%O A127448 1,3
%A A127448 _Gary W. Adamson_, Jan 14 2007
%E A127448 Converted comments to formulas, extended - _R. J. Mathar_, Sep 11 2009
%E A127448 Corrected A-number typo in a formula - _R. J. Mathar_, Sep 17 2009
%E A127448 Corrected last example line by _John Mason_, Jan 07 2015